Thread: Calculus Question

Population grows according to the equation , where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is


(a) 0.069 (b) 0.200 (c) 0.301 (d) 3.322 (e) 5.000

Originally Posted by frozenflames

Population grows according to the equation , where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is

(a) 0.069 (b) 0.200 (c) 0.301 (d) 3.322 (e) 5.000

Hello,

the growth of this population can be described by the equation:


where p is the actual amount, is the starting value.

Put in the values you know:


solve for k:

now you have to use a caculator or a logarthmic table.

You'll get
that means that none of the given results seem to be right.

Greetings

EB

Greetings EB:

I solved for k in the equation P(t) = P_0 e^kt which yields k = 0.1*ln(2) approx= 0.069. As it happens, 0.069 is indeed one of the indicated choices.

Enjoy the day,

Rich B.

Originally Posted by Rich B.

Greetings EB:

I solved for k in the equation P(t) = P_0 e^kt which yields k = 0.1*ln(2) approx= 0.069. As it happens, 0.069 is indeed one of the indicated choices.

Enjoy the day,

Rich B.

Hello, RichB.

of course you are right - BUT. when frozenflames referred to the equation I was not aware, that the equation was meant which you used. It all depends on the base you choose for solving this problem. I have choosen for 10 and thats why I came up with a "wrong" result.

Have a nice day too.

EB

Originally Posted by earboth

Hello, RichB.

of course you are right - BUT. when frozenflames referred to the equation I was not aware, that the equation was meant which you used. It all depends on the base you choose for solving this problem. I have choosen for 10 and thats why I came up with a "wrong" result.

Have a nice day too.

EB

In fact it does not matter (in principle) what you take for
(as long as it is positive ) in a growth equation of the form:



for:



Here there is a good case for using 2 since we are discussing doubling
times, so here it might be natural to use:



RonL

Hi Ron:

Right you are. I was just fishing for a base that would yield a parameter, k, that appears in the multiple choice list.

Enjoy.

Rich